The Distribution of Solutions of the Congruence x1x2x3... x$_{n}\equiv $c (mod p)

For a cube B of size B, we obtain a lower bound on B so that B ∩ V is nonempty, where V is the algebraic subset of Fp ndefined by x1x2x3... x$_{n}\equiv $c (mod p), n a positive integer and c an integer not divisible by p. For n = 3 we obtain that B ∩ V is nonempty if B ≫ p2/3(log p)2/3, for n = 4 we obtain that B ∩ V is nonempty if B$\gg \sqrt{p}$logp, and for n ≥ 5 we obtain that B ∩ V is nonempty if B ≫ p$^{\frac{1}{4}+\frac{1}{\sqrt{2(n+4)}}}$(log p)3/2. Using the assumption of the Grand Riemann Hypothesis we obtain B ∩ V is nonempty if B ≫εp2/n+ε.